find the constant : x:2,8,16 y:9,36,72
To find the constant, we can use the formula for a straight line: y = mx + b, where m is the slope and b is the y-intercept.
Using the given data points:
For x = 2, y = 9:
9 = 2m + b (equation 1)
For x = 8, y = 36:
36 = 8m + b (equation 2)
For x = 16, y = 72:
72 = 16m + b (equation 3)
We can subtract equation 1 from equation 2 to eliminate the y-intercept:
36 - 9 = 8m - 2m + b - b
27 = 6m
m = 27/6
m = 4.5
Now, substitute the value of m back into any one of the original equations to find the value of b. Let's use equation 1:
9 = 2(4.5) + b
9 = 9 + b
b = 9 - 9
b = 0
Therefore, the constant (b) is 0.